A system for generating or reproducing sound, including amplifiers, cables and loudspeakers, will always affect the spectral properties of the sound, often in unwanted ways. The reverberation of the room where the equipment is placed adds further modifications. Sound reproduction with very high quality can be attained by using matched sets of cables, amplifiers and loudspeakers of the highest quality, but this is cumbersome and very expensive. The increasing computational power of PCs and digital signal processors has introduced new possibilities for modifying the characteristics of a sound generating or sound reproducing system. The dynamic properties of the sound generating system may be measured and modeled by recording its response to known test signals, as well known from the literature. A precompensation filter, R in FIG. 1, is then placed between the original sound source and the audio equipment. The filter is calculated and implemented to compensate for the measured properties of the sound generating system, symbolized by H in FIG. 1. In particular, it is desirable that the phase and amplitude response of the compensated system is close to a prespecified ideal response, symbolized by D in FIG. 1. In other words, it is thus required that the compensated sound reproduction y(t) matches the ideal yref(t) to some given degree of accuracy. The pre-distortion generated by the precompensator R cancels the distortion due to the system H, such that the resulting sound reproduction has the sound characteristic of D. Up to the physical limits of the system, it is thus, at least in theory, possible to attain a superior sound quality, without the high cost of using extreme high-end audio equipment. The aim of the design could, for example, be to cancel acoustic resonances caused by imperfectly built loudspeaker cabinets. Another application could be to minimize low-frequency resonances due to the room acoustics, in different places of the listening room.
Digital precompensation filters can be applied not only to a single loudspeaker but also to multichannel sound generating systems. They can be important elements of designs aimed not only to generate better sound, but also to produce specific effects. The generation of virtual sound sources, rendering of sound, is of interest in, for example, the audio effects of computer games.
There has since a long time existed equipment, called graphical equalizers, aimed at compensating the frequency response of a sound generating system by modifying its gains in a set of fixed frequency bands. Automatic schemes exist that adjust such filters, see e.g. [1]. There are also other prior art techniques that partition the audio frequency range into different frequency bands, and construct different compensators within each of these bands, see e.g. [2, 3]. Such sub-band solutions will suffer from inadequate phase compensation, which creates problems, in particular at the borders of the bands.
Methods that treat the audio frequency range of interest as one band, have been suggested. This requires the use and adjustment of filters with a very high number of adjustable coefficients. Proposed methods are in general based on the adjustment of FIR (Finite Impulse Response) filters to minimize a least squares criterion that measures the deviation between the compensated signal y(t) and the desired response yref(t). See e.g. [4–10]. This formulation has been considered attractive since there exist tractable adaptation algorithms, as well as off-line design algorithms, that can adjust FIR filters based on least squares criteria. There also exist proposals for non-linear compensators, see e.g. [11]. Solutions, which suggest separate measurements of the room acoustics response and the loudspeaker response, have also been used in the design of a precompensation inverse filter for sound reproduction systems [3, 12]. This design partly equalizes both responses. In [13] a method is disclosed that apply both FIR and IIR (Infinite Impulse Response) filters in audio system compensation. Such an approach is used to reduce the required number of FIR filter parameters in the compensation filter. However, all these present methods suffer from significant difficulties, which make their practical use quite problematic. The design schemes available in prior art generally result in compensation filters that have a high computational complexity and severe practical limitations. The resulting automatically generated compensation filters are sometimes even dangerous to the audio equipment, due to the risk of generating compensation signals with too high power.